Method and apparatus for viterbi detection of generalized partial response signals using partial matched filter and matched filter metrics

ABSTRACT

Methods and apparatus are provided for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals using both partial matched filter and matched filter metrics. In the method of the invention, branch metric terms are transformed to shift all time varying terms and some constant terms after an add compare select (ACS) unit. The total number of non-zero constants on trellis branches is minimized. The shifted time varying terms and the shifted constant terms are added directly to state metric terms. The time varying terms are expressed as outputs Z n  of a partial matched filter or as outputs W n  of a matched filter. For a given generalized partial response target, the time-invariance property of the Viterbi detector enables identifying the minimum number of non-zero constants on trellis branches without resorting to heuristics. The time-invariance property holds for Viterbi detectors that process multiple samples per trellis-branch, thus allowing implementations at any desired speed.

FIELD OF THE INVENTION

The present invention relates generally to data detection methods and apparatus for generalized partial-response channels in a direct access storage device, and more particularly, relates to a general methodology and apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals using transformed metrics, such as, the partial matched filter branch metrics and the matched filter branch metrics.

DESCRIPTION OF THE RELATED ART

Partial-response signaling with maximum-likelihood sequence detection techniques are known for digital data communication and recording applications.

U.S. Pat. No. 5,619,539 discloses data detection methods and apparatus for a direct access storage device including an 8-state extended partial-response class 4 (EPR4) trellis with modified branch metrics based upon heuristics so that the number of nonzero trellis branch constants is reduced.

U.S. Pat. No. 5,430,744 discloses a Viterbi decoder having a recursive processor modified to process each node in a trellis of a partial-response coded signal via heuristics to shift the branch metric additions over the node to effectuate compare, select, add operation order on the predecessor survivor metrics terminating in that node, to compare the metrics of the predecessor sequences terminating in the node, to select a survivor sequence, and to add the shifted branch metrics to the metric of the selected survivor sequence.

A need exists for a methodology for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial-response signals. It is desirable to provide a general methodology and apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals using the partial matched filter branch metrics and the matched filter branch metrics.

SUMMARY OF THE INVENTION

A principal object of the present invention is to provide a methodology for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals including both partial matched filter and matched filter. Other important objects of the present invention are to provide Viterbi detectors for generalized partial response signals including both partial matched filter and matched filter branch metrics substantially without negative effect and that overcome many of the disadvantages of prior art arrangements.

In brief, methods and apparatus are provided for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals including both partial matched filter and matched filter branch metrics. In the method of the invention, branch metric terms are transformed to shift all time varying terms and some constant terms after an add compare select (ACS) unit. A total number of non-zero constants on trellis branches are minimized. The shifted time varying terms and the shifted constant terms are added directly to state metric terms.

In accordance with features of the invention, the time varying terms are expressed as outputs Z_(n) of a partial matched filter or as outputs W_(n) of a matched filter. For a given generalized partial response target, the time-invariance property of the Viterbi detector enables identifying the minimum number of non-zero constants on trellis branches without resorting to heuristics. The time-invariance property holds for Viterbi detectors that process multiple samples per trellis-branch, thus allowing implementations at any desired speed.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention together with the above and other objects and advantages may best be understood from the following detailed description of the preferred embodiments of the invention illustrated in the drawings, wherein:

FIG. 1 is a block diagram representation illustrating a generalized partial-response data channel including a NPML 16-state detector for PR4 equalized signals using partial matched filter metric in accordance with the preferred embodiment;

FIG. 2 illustrates a NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment;

FIG. 3 illustrates a transformed NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment;

FIG. 4 illustrates an equivalent NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment;

FIG. 5 illustrates another equivalent NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment;

FIG. 6 is a block diagram representation illustrating a generalized partial-response data channel including a NPML 16-state detector for PR4 equalized signals using matched filter metric in accordance with the preferred embodiment;

FIG. 7 illustrates a NPML 16-state detector for EPR4 equalized signals using matched filter metric in accordance with the preferred embodiment;

FIG. 8 illustrates a NPML 16-state trellis with matched filter metric in accordance with the preferred embodiment;

FIG. 9 illustrates a transformed NPML 16-state trellis with matched filter metric in accordance with the preferred embodiment;

FIG. 10 illustrates an equivalent NPML 16-state trellis with matched filter metric in accordance with the preferred embodiment;

FIG. 11 illustrates is a block diagram representation illustrating a generalized partial-response data channel including a EPR4 detector for PR4 equalized signals using matched filter metric in accordance with the preferred embodiment;

FIG. 12 illustrates is a block diagram representation illustrating a generalized partial-response data channel including an EPR4 detector for PR4 equalized signals using matched filter metric in accordance with the preferred embodiment;

FIG. 13 illustrates an EPR4 2T trellis with partial matched filter metric in accordance with the preferred embodiment;

FIG. 14 illustrates an equivalent EPR4 2T trellis with partial matched filter metric in accordance with the preferred embodiment;

FIG. 15 illustrates is a block diagram representation illustrating a generalized partial-response data channel including an EPR4 detector for EPR4 equalized signals using partial matched filter metric in accordance with the preferred embodiment;

FIG. 16 illustrates is a block diagram representation illustrating a generalized partial-response data channel including an EPR4 detector for EPR4 equalized signals using matched filter metric in accordance with the preferred embodiment;

FIG. 17 illustrates an EPR4 2T trellis with matched filter metric in accordance with the preferred embodiment;

FIG. 18 illustrates a NPML 16-state 2T trellis with partial matched filter metric in accordance with the preferred embodiment;

FIG. 19 illustrates a NPML 16-state 2T trellis with matched filter metric in accordance with the preferred embodiment; and

FIGS. 20 and 21 illustrate add compare select (ACS) units in accordance with the preferred embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In accordance with features of the invention, a general methodology for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial-response signals is provided. Optimization of the Viterbi detector architecture achieves substantial reduction in hardware complexity and power consumption. The conventional Viterbi detector operating on an arbitrary generalized partial-response target with L coefficients requires 2^(L) states with 2^(L+1) branch metrics of the form ay_(n)+c where the constants a and c are not necessarily the same for each trellis branch.

In accordance with features of the invention, the branch metrics are transformed so that some of the constant terms and all of the data dependent or time-varying terms are shifted after the add/compare/select (ACS) unit and added directly to the state metrics. There are only 2^(L−1) additions with data dependent or time-varying terms and at most 2^(L−1) additions with constant terms after the add/compare/select (ACS) units. Furthermore, the branch metrics themselves become constants. There are only 2^(L−1) non-zero constants as branch metrics.

In accordance with features of the invention, it is shown that the state metrics of a Viterbi detector possess a time-invariance property which together with the distributive law min(a+x,b+x)=min(a,b)+x allows to shift the data dependent or time-varying terms of the branch metrics to the output of the add-compare-select (ACS) units and to also minimize the total number of non-zero constants on the trellis branches. For a given generalized partial response target the time-invariance property guarantees how to systematically find the minimum number of non-zero constants associated with the branch adders without resorting to heuristics. Furthermore, it provides a method for exhaustively determining all possible realizations of the data dependent or time-varying terms of the branch metrics, expressed as outputs of matched-filters or partial matched-filters. The time-invariance property also holds for Viterbi detectors that process multiple samples per trellis-branch thus allowing implementations at any desired speed. The application of the general methodology is illustrated with specific embodiments related to noise-predictive maximum-likelihood (NPML) or “fractional coefficient” detection with targets of the form (1−D²) (1+p1D+p2D²) where p1 and p2 are arbitrary real numbers, not necessarily integers, with the corresponding detectors operating on a T or 2T basis, and extended partial response class 4 (EPR4) targets with a Viterbi detector operating on a 2T basis, where 1/T is the sample rate.

Consider a generalized partial response (PR) shaped signal in the presence of noise, that is: $\begin{matrix} {y_{n} = {a_{n} + {\sum\limits_{i = 1}^{L}{f_{i}a_{n - i}}} + \eta_{n}}} & (1) \end{matrix}$

where a_(n) is the data symbol at time nT, F(D)=(1+f₁D+f₂D²+ . . . +f_(L)D^(L)) is the generalized PR polynomial and η_(n) is the noise sample at the input of the detector. The Viterbi detector operating on y_(n) will find the sequence {â_(n)} that minimizes the following metric: $\begin{matrix} {J = {\sum\limits_{n}\left\{ {y_{n} - \left( {a_{n} + {\sum\limits_{i = 1}^{L}{f_{i}a_{n - i}}}} \right)} \right\}^{2}}} & (2) \end{matrix}$

or equivalently minimize the metric: $\begin{matrix} {J = {{{- 2}{\sum\limits_{n}{y_{n}\left( {a_{n} + {\sum\limits_{i = 1}^{L}{f_{i}a_{n - i}}}} \right)}}} + {\sum\limits_{n}\left( {a_{n} + {\sum\limits_{i = 1}^{L}{f_{i}a_{n - i}}}} \right)^{2}}}} & (3) \end{matrix}$

For saturation recording systems the channel input an is binary, that is +1 or −1. In this case the metric in equation (3) is simplified to $\begin{matrix} {J = {{- {\sum\limits_{n}{y_{n}\left( {a_{n} + {\sum\limits_{i = 1}^{L}{f_{i}a_{n - i}}}} \right)}}} + {\sum\limits_{n}\left( {{\sum\limits_{i = 1}^{L}{f_{i}a_{n}a_{n - i}}} + {\sum\limits_{i = 1}^{L - 1}{\sum\limits_{j > 1}^{L}{f_{i}f_{j}a_{n - i}a_{n - j}}}}} \right)}}} & (4) \end{matrix}$

where the first sum contains terms that depend on the channel output, referred to as data dependent or time-varying terms, and the second sum contains terms that do not depend on the channel output, referred to as constants. The following property is crucial in simplifying the architecture/implementation of the Viterbi detector. Observe that in general: $\begin{matrix} {{\sum\limits_{n = 0}^{\infty}{y_{n}a_{n - i}}} = {{\sum\limits_{n = {- i}}^{\infty}{y_{n + i}a_{n}}} = {\sum\limits_{n = 0}^{\infty}{y_{n + i}a_{n}}}}} & (5) \end{matrix}$

is valid, where the last equality holds because of causality, i.e., a_(n)=0 for n<0. The property stated in equation (5) is called the “time-invariance” property of the state metrics. Note that this property can be independently applied to the two summation terms in equation (4). For a channel memory of L symbols, equation (5) suggests that there are L! possible sets of data dependent or time-varying branch metric terms and $\prod\limits_{i = 0}^{L - 1}\left( {L - i} \right)^{L - i}$

possible sets of branch constants within the window an, a_(n, . . .) , a_(n−L). In order to optimize the Viterbi detector architecture with respect to speed and area one has to identify the set of data dependent or time-varying branch metric terms that shifts after the ACS unit and the set of branch metric constants with the maximum number of zeros. Since the set of all possible combinations is well defined and finite, the desired set of constants with the maximum number of zeros can be found, for example, via a computer search.

Consider now matched filter and partial matched filter transformations. Applying the time-invariance property to the first summation term in equation (4) one obtains: $\begin{matrix} {J = {{- {\sum\limits_{n}{a_{n}\left( {y_{n} + {\sum\limits_{i = 1}^{L}{f_{i}y_{n + i}}}} \right)}}} + {\sum\limits_{n}\left( {{\sum\limits_{i = 1}^{L}{f_{i}a_{n}a_{n - i}}} + {\sum\limits_{i = 1}^{L - 1}{\sum\limits_{j > 1}^{L}{f_{i}f_{j}a_{n - i}a_{n - j}}}}} \right)}}} & (6) \\ {Let} & \quad \\ {W_{n} = {y_{n} + {\sum\limits_{i = 1}^{L}{f_{i}y_{n + i}}}}} & (7) \end{matrix}$

Clearly, W_(n) represents the output of a filter matched to the generalized PR channel polynomial F(D). Substituting equation (7) into equation (6) we obtain: $\begin{matrix} {J = {{- {\sum\limits_{n}{a_{n}W_{n}}}} + {\sum\limits_{n}\left( {{\sum\limits_{i = 1}^{L}{f_{i}a_{n}a_{n - i}}} + {\sum\limits_{i = 1}^{L - 1}{\sum\limits_{j > i}^{L}{f_{i}f_{j}a_{n - i}a_{{n - j}\quad}}}}} \right)}}} & (8) \end{matrix}$

The above transformed metric achieves that the channel output dependent term of the branch metric, i.e., a_(n) W_(n) can be shifted after the ACS unit leaving on the trellis branches only constants.

Consider, as a second example, a generalized PR polynomial of the following form:

F(D)=(1−D²)(1+p₁D+p₂D²+ . . . +p_(L−2)D^(L−2))=(1−D²)p(D)  (9)

where the coefficients p₁, p₂, . . . p_(L−2) are usually selected so that the noise at the input of the detector is as white as possible. In this case the coefficients p₁,p₂, . . . p_(L−2) are the predictor coefficients and the polynomial P(D) is the whitening filter of order L−2. In this example let $\begin{matrix} {Z_{n} = {y_{n} + {\sum\limits_{i = 1}^{L - 2}{p_{i}y_{n + i}}}}} & (10) \end{matrix}$

denote the output of a filter which is matched only to the filter P(D), so that it is partially matched to the channel polynomial F(D). Using the time-invariance property stated in equation (5) and the partial matched-filter signal Z_(n) the following equivalent metric is obtained: $\begin{matrix} {J = {{- {\sum\limits_{n}{\left( {a_{n} - a_{n - 2}} \right)Z_{n}}}} + {\sum\limits_{n}\left( {{\sum\limits_{i = 1}^{L}{f_{i}a_{n}a_{n - i}}} + {\sum\limits_{i = 1}^{L - 1}{\sum\limits_{j > i}^{L}{f_{i}f_{j}a_{n - i}a_{n - j}}}}} \right)}}} & (11) \end{matrix}$

As in the matched-filter case, the transformed metric in equation (11) achieves that the channel output dependent term of the branch metric, that is, Z_(n)(a_(n)−a_(n−2)) can be shifted after the ACS units leaving on the trellis branches only constants. Clearly, there are other partial matched-filter transformations that can be applied to the metric in equation (6) such as, (1−D)P(D), (1+D)P(D), and the like.

Applying the time-invariance property to the second summation term in equation (8) so that a_(n) comes out as a common factor we obtain the equivalent metric: $\begin{matrix} {J = {{- {\sum\limits_{n}{a_{n}W_{n}}}} + {\sum\limits_{n}\left( {a_{n}\left( {\sum\limits_{i = 1}^{L}{s_{i}a_{n - i}}} \right)} \right.}}} & (12) \end{matrix}$

where s_(i), i=1, 2, . . . , L are the one sided coefficients of the autocorrelation function of the generalized PR polynomial F(D), that is: $\begin{matrix} {{s_{i} = {f_{i} + {\sum\limits_{j = 1}^{{i + j} \leq L}{f_{j}f_{i + j}}}}},\quad {i = 1},2,\ldots \quad,L} & (13) \end{matrix}$

This particular metric in equation (12) is known in the literature as the matched filter metric.

In accordance with preferred embodiments for T-processing, for NPML or “fractional-target” 16-state detection with two predictor coefficients the target function is:

F(D)=(1−D²)(1+p₁D+p₂D²)=(1−D²)P(D)  (14)

Let S(D)=F(D) F(D⁻¹) be the D-transform of the autocorrelation function of the impulse response associated with the detector target. Then,

S(D)=s₄D⁻⁴⁺s₃D⁻³⁺s₂D⁻²⁺s₁D⁻¹⁺s₀+s₁D¹⁺s₂D²⁺s₃D³⁺s₄D⁴  (15)

where,

s₁=p₁(p₂+1),

s₂=−(1−p₂)²−p₁ ²

s₃=−p₁(p₂+1),

s4=−p₂  (16)

In this case by applying the time-invariance transformation, the following equivalent matched-filter metric is obtained $\begin{matrix} {J = {{- {\sum\limits_{n}{\left( {a_{n} - a_{n + 1}} \right)Z_{n}}}} + {\sum\limits_{n}\left\{ {{s_{1}a_{n}a_{n - 1}} + {\left( {s_{2} + s_{4}} \right)a_{n}a_{n - 2}} - {s_{1}a_{n}a_{n - 3}} + {s_{4}a_{n}a_{n - 4}} - {s_{1}a_{n - 1}a_{n - 2}} + {s_{1}a_{n - 2}a_{n - 3}} - {s_{4}a_{n - 2}a_{n - 4}} + s_{4}} \right\}}}} & (17) \end{matrix}$

Having reference now to the drawings, in FIG. 1, there is shown a generalized partial-response data channel of the preferred embodiment generally designated by the reference character 100. As shown in FIG. 1, a readback signal is applied to a low pass filter 102 and applied to a PR4 equalizer 104. The PR4 equalizer 104 is followed by a whitening/predictor filter 1+p1D+p2D² 106, a partial matched filter (1−D⁻¹)(1+p1D⁻¹+p2D⁻²) 108, and a corresponding 16-state noise-predictive maximum-likelihood (NPML) detector 110. The output of PR4 equalizer 104 is an equalized signal x_(n). The output of the whitening/predictor filter 1+p1D+p2D² 106 is the whitened output y_(n). The partial matched-filter (1−D⁻¹) (1+p1D⁻¹+p2D⁻²) 108 facilitates the transformation of the trellis according to the metric in equation (17) providing an output Z_(n). The 16-state NPML detector 110 provides output decisions a_(n).

FIG. 2 illustrates a NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 200. Transitioning through the trellis 200 from time nT represented by the nodes on the left hand side of the trellis to time (n+1)T represented by the nodes on the right hand side of the trellis, Add-Compare-Select (ACS) operations are performed to find the updated state metric. As shown in FIG. 2, NPML 16-state trellis with partial matched filter metric 200 includes 16 nodes or states and 32 branches connecting the 16 states together between time steps. The values a_(n−4)a_(n−3)a_(n−2)a_(n−1) and a_(n−3)a_(n−2)a_(n−1)a_(n) are the trellis states (0-15) at times nT and (n+1)T, respectively. On the right side of the trellis, branch metric data dependent terms (+2Z_(n), −2Z_(n)) 202 and branch metric constant terms (combinations of s₁, s₂, s₄) 204 are shown. The output Z_(n) of partial matched-filter (1−D⁻¹)(1+p1D⁻¹+p2D⁻²) 108 is shown above the trellis.

FIG. 3 illustrates a transformed NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 300. As shown in FIG. 3, the NPML 16-state trellis with partial matched filter metric 200 of FIG. 2 is transformed by subtracting the constant term s₂+2s₄ from all the state metrics and normalizing all metric components by a factor of two. The resulting branch metric data dependent terms (+Z_(n), −Z_(n)) 302 and branch metric constant terms (combinations of s₁, s₂, s₄) 304 are shown on the right side of the trellis 300.

Referring to FIGS. 4 and 5, FIG. 4 illustrates an equivalent NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 400. FIG. 4 shows the 16-state trellis 400 where the common data dependent terms and constant terms have been collected at the output of the ACS units by applying the distributive law min(a+x, b+x)=min(a,b)+x. FIG. 5 illustrates another equivalent NPML 16-state trellis with partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 500. Both trellises 400 and 500 require only 8 branch adders instead of 32 for the branch metric data dependent terms (+Z_(n), −Z_(n)) 302. Furthermore, there are 4 additions with the branch metric data dependent terms +Z_(n) 402, 502, 4 additions with the branch metric data dependent terms −Z_(n) 402, 502, and 6 additions with branch metric constant terms 404, 504 following the ACS unit that involve only three constants, s₁, s₂, s₄.

An equivalent metric realization can be obtained by applying a full matched-filter transformation to the metric in equation (4). By applying the time-invariance transformation we obtain the following equivalent matched-filter metric: $\begin{matrix} {J = {{- {\sum\limits_{n}{a_{n}W_{n}}}} + {\sum\limits_{n}\left( {a_{n}\left( {\sum\limits_{i = 1}^{4}{s_{i}a_{n - i}}} \right)} \right.}}} & (18) \end{matrix}$

FIG. 6 is a block diagram representation illustrating a generalized partial-response data channel including a NPML 16-state detector for PR4 equalized signals using matched filter metric in accordance with the preferred embodiment generally designated by the reference character 600. As shown in FIG. 6, a readback signal is applied to a low pass filter 102 and applied to a PR4 equalizer 104. The PR4 equalizer 104 is followed by a whitening/predictor filter 1+p1D+p2D² 106, a matched filter (1+p1D⁻¹+p2D⁻²)(1−D⁻²) 608, and a corresponding 16-state noise-predictive maximum-likelihood (NPML) detector 610. The output of PR4 equalizer 104 is an equalized signal x_(n). The output of the whitening/predictor filter 1+p1D+p2D² 106 is the whitened output y_(n). The matched-filter (1+p1D⁻¹+p2D⁻²) (1−D⁻²) 108 facilitates the transformation of the trellis according to the metric in equation (18) providing an output W_(n). The 16-state NPML detector 610 provides output decisions a_(n).

FIG. 7 illustrates a NPML 16-state detector for extended PR4 (EPR4) equalized signals using matched filter metric in accordance with the preferred embodiment generally designated by the reference character 700. As shown in FIG. 7, a readback signal is applied to a low pass filter 102 and applied to an EPR4 equalizer 704. The EPR4 equalizer 704 replaces the PR4 equalizer 104 of FIG. 6. The EPR4 equalizer 704 is followed by a matched filter (1+p1D+p2D²)(1+p1D⁻¹+p2D⁻²)(1−D⁻¹) 708, and a corresponding 16-state noise-predictive maximum-likelihood (NPML) detector 710. The output of EPR4 equalizer 704 is an equalized signal x_(n). The matched-filter (1+p1D+p2D²)(1+p1D⁻¹+p2D⁻²)(1−D⁻¹) 708 provides an output W_(n). The 16-state NPML detector 710 provides output decisions a_(n).

Referring now to FIGS. 8, 9 and 10, FIG. 8 illustrates a NPML 16-state trellis with matched filter metric in accordance with the preferred embodiment generally designated by the reference character 800. On the right side of the trellis 800, branch metric data dependent terms (+W_(n), −W_(n)) 802 and branch metric constant terms (combinations of s₁, s₂, s₃, s₄) 804 are shown. FIG. 8 shows the 16-state T-trellis 800 that minimizes the metric in equation (18). FIG. 9 illustrates a transformed NPML 16-state T-trellis with matched filter metric in accordance with the preferred embodiment generally designated by the reference character 900. FIG. 9 shows the trellis in FIG. 8 after adding the term W_(n)−s₁−s₂−s3−s4 to all the state metrics. In FIG. 9, the data dependent branch metric term 2W_(n) 902 is associated with states 0-7 and the constant branch metric terms (combinations of s₁,s₂,s₃,s₄) 904 are associated with states 0-15. FIG. 10 illustrates an equivalent NPML 16-state T-trellis with matched filter metric and a two-way add/compare/select (ACS) in accordance with the preferred embodiment generally designated by the reference character 1000. FIG. 10 shows the resulting 16-state trellis 1000 after collecting the common data dependent or time-varying and constant terms at the output of the ACS units according to the distributive law min(a+x, b+x)=min(a,b)+x, and normalizing all metric components by a factor of two. In FIG. 10, the data dependent branch metric term +W_(n) 1002 is associated with states 0-7 and the constant branch metric terms (combinations of s₁,s₂,s₃,s₄) 1004 are associated with states 8-15 only. In the trellis of FIG. 10 there are only 8 branch adders instead of 32. There are 8 additions with the data dependent term +W_(n) 1002 and 6 additions with constant terms (combinations of s₁,s₂,s₃,s₄) 1004 following the ACS unit. From equation (16), note that s₁+s₃ equals zero.

Consider the time-invariance property for 2T-processing. High data rates may necessitate the processing of multiple samples per trellis branch. In the following, it is described how the concept of time invariance of the state metrics applies to the case of processing two samples per trellis branch. The extension of this concept to processing any number of samples per trellis branch is straight forward. A Viterbi detector operating on two samples at a time, will find the sequence that minimizes the following metric: $\begin{matrix} {J = {{- {\sum\limits_{n}{y_{n}\left( {a_{2n} + {\sum\limits_{i = 1}^{L}{f_{i}a_{{2n} - i}}}} \right)}}} - {\sum\limits_{n}{y_{{2n} + 1}\left( {a_{{2n} + 1} + {\sum\limits_{i = 1}^{L}{f_{i}a_{{2n} + 1 - i}}}} \right)}} + {\sum\limits_{n}\left( {{\sum\limits_{i = 1}^{L}{f_{i}a_{2n}a_{{2n} - i}}} + {\sum\limits_{i = 1}^{L - 1}{\sum\limits_{j > i}^{L}{f_{i}f_{j}a_{{2n} - i}a_{{2n} - j}}}}} \right)} + {\sum\limits_{n\quad}\left( {{\sum\limits_{i = 1}^{L}{f_{i}a_{{2n} + 1}a_{{2n} + 1 - i}}} + {\sum\limits_{i = 1}^{L - 1}{\sum\limits_{j > i}^{L}{f_{i}f_{j}a_{{2n} + 1 - i}a_{{2n} + 1 - j}}}}} \right)}}} & (19) \end{matrix}$

Observe that: $\begin{matrix} {{\sum\limits_{n = 0}^{\infty}{y_{n}a_{{2n} - {2j} - i}}} = {{\sum\limits_{n = {- j}}^{\infty}{y_{{2n} + {2j}}a_{{2n} - i}}} = {\sum\limits_{n = 0}^{\infty}{y_{{2n} + {2j}}a_{{2n} - i}}}}} & (20) \end{matrix}$

Similarly: $\begin{matrix} {{\sum\limits_{n = 0}^{\infty}{y_{{2n} + 1}a_{{2n} - {2j} - i}}} = {{\sum\limits_{n = {- j}}^{\infty}{y_{{2n} + {2j} + 1}a_{{2n} - i}}} = {\sum\limits_{n = 0}^{\infty}{y_{{2n} + {2j} + 1}a_{{2n} - i}}}}} & (21) \end{matrix}$

where i=0,1. Thus, the time-invariance property now holds on a two-step basis for both the odd and even sequence of channel output samples. In general, when processing m samples per trellis branch the time-invariance property holds on an m-step basis.

The preferred embodiments for 2T-processing may be understood as follows. The EPR4 detector target is given by, F(D)=(1−D²)(1+D)=(1+D−D²−D³). This target gives rise to an 8-state trellis. A Viterbi detector operating on two samples, y_(2n), y_(2n+1) at a time, will find the sequence {â_(n)} that according to equation (19) minimizes the following metric $\begin{matrix} {J = {{- {\sum\limits_{n}\left\{ {{y_{2n}\left( {a_{2n} + a_{{2n} - 1} - a_{{2n} - 2} - a_{{2n} - 3}} \right)} + {y_{{2n} + 1}\left( {a_{{2n} + 1} + a_{2n} - a_{{2n} - 1} - a_{{2n} - 2}} \right)}} \right\}}} + {\sum\limits_{n}\left( {{{- 2}a_{2n}a_{{2n} - 2}} - {a_{2n}a_{{2n} - 3}} - {a_{{2n} - 1}a_{{2n} - 3}} + {a_{{2n} - 2}a_{{2n} - 3}} + {a_{{2n} + 1}a_{2n}} - {a_{{2n} + 1}a_{{2n} - 1}} - {a_{{2n} + 1}a_{{2n} - 2}}} \right)}}} & (22) \end{matrix}$

As can be seen the first summation term in equation (22) depends on the channel samples and has been termed the data dependent or time-varying component of the branch metric. The second summation term depends only on data symbols and has been termed the constant component of the branch metric. Applying the time-invariance equation to the first summation term in equation (22) we obtain: $\begin{matrix} {{- {\sum\limits_{n}\left\{ {{y_{2n}\left( {a_{2n} + a_{{2n} - 1} - a_{{2n} - 2} - a_{{2n} - 3}} \right)} + {y_{{2n} + 1}\left( {a_{{2n} + 1} + a_{2n} - a_{{2n} - 1} - a_{{2n} - 2}} \right)}} \right\}}} = {- {\sum\limits_{n}\left\{ {{\left( {a_{2n} + a_{{2n} - 1}} \right)Z_{2n}} + {\left( {a_{{2n} + 1} + a_{2n}} \right)Z_{{2n} + 1}}} \right\}}}} & (23) \end{matrix}$

where Zn=y_(n)−y_(n+2) can be interpreted as the output of a partial matched-filter with a response matched to 1−D².

As described above, there are only a finite number of possible sets of branch constants for the transition defined by the window of symbols a_(2n−3), . . . , a_(2n+1) which can be exhaustively found by computer search exploiting the time-invariance property in equations (20) and (21). It can readily be seen that there are only 16 sets of constants. Out of the 16 possible sets of constants the one leading to the set with the maximum number of zeros corresponds to the RHS of the following equation $\begin{matrix} {{\sum\limits_{n}\left( {{{- 2}a_{2n}a_{{2n} - 2}} - {a_{2n}a_{{2n} - 3}} - {a_{{2n} - 1}a_{{2n} - 3}} + {a_{{2n} - 2}a_{{2n} - 3}} + {a_{{2n} + 1}a_{2n}} - {a_{{2n} + 1}a_{{2n} - 1}} - {a_{{2n} + 1}a_{{2n} - 2}}} \right)} = {\sum\limits_{n}\left( {{{- 2}a_{2n}a_{{2n} - 2}} - {a_{2n}a_{{2n} - 3}} - {2a_{{2n} + 1}a_{{2n} - 1}} + {a_{{2n} - 2}a_{{2n} - 3}} + {a_{{2n} + 1}a_{2n}} - {a_{{2n} + 1}a_{{2n} - 2}}} \right)}} & (24) \end{matrix}$

Combining the data dependent and constant terms in equations (23) and (24), respectively, we obtain the following equivalent partial matched-filter metric for EPR4 detectors processing two samples per trellis branch: $\begin{matrix} {J = {{- {\sum\limits_{n}\left\{ {{\left( {a_{2n} + a_{{2n} - 1}} \right)Z_{2n}} + {\left( {a_{{2n} + 1} + a_{2n}} \right)Z_{{2n} + 1}}} \right\}}} + {\sum\limits_{n}\left( {{{- 2}a_{2n}a_{{2n} - 2}} - {a_{2n}a_{{2n} - 3}} - {2a_{{2n} + 1}a_{{2n} - 1}} + {a_{{2n} - 2}a_{{2n} - 3}} + {a_{{2n} + 1}a_{2n}} - {a_{{2n} + 1}a_{{2n} - 2}}} \right)}}} & (25) \end{matrix}$

Referring now to FIGS. 11, 12, 13, and 14, FIG. 11 shows a block diagram representation illustrating a generalized partial-response data channel including a EPR4 detector for PR4 equalized signals using matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1100. As shown in FIG. 11, a readback signal is applied to a low pass filter 102 and applied to a PR4 equalizer 104. The PR4 equalizer 104 is followed by an EPR4 shaping filter 1+D 1106, a partial matched filter 1−D⁻² 1108, and a corresponding 8-state EPR4 detector 1110. The output of PR4 equalizer 104 is an equalized signal x_(n). The output of the EPR4 shaping filter 1+D 1106 is the output y_(n). The partial matched filter 1−D⁻² 1108 provides an output Z_(n). The 8-state EPR4 detector 1110 provides output decisions a_(n). The EPR4 shaping filter 1+D 1106 facilitates the transformation of the trellis according to the metric in equation (25).

FIG. 12 shows a block diagram representation illustrating a generalized partial-response data channel including an EPR4 detector for EPR4 equalized signals using partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1200. As shown in FIG. 12, the low pass filter 102 and the PR4 equalizer 104 is followed by an EPR4 shaping filter 1+D 1206, a partial matched filter (1−D⁻²)(1−D⁻¹) 1208, and a corresponding 8-state EPR4 detector 1210. The output of PR4 equalizer 104 is an equalized signal x_(n). The output of the EPR4 shaping filter 1+D 1106 is the output y_(n). The partial matched filter (1−D⁻²)(1−D⁻¹) 1208 provides an output W_(n). The 8-state EPR4 detector 1210 provides output decisions a_(n).

FIG. 13 illustrates an EPR4 2T trellis with partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1300 including data dependent branch metrics 1302 and constant branch metrics 1304. FIG. 13 shows the 8-state trellis 1300 that minimizes the metric in equation (25) where the common data dependent or time-varying terms 1302 have been collected at the output of the ACS units according to the distributive law min(a+x, b+x)=min(a,b)+x.

FIG. 14 illustrates an equivalent EPR4 2T trellis with partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1400 including data dependent branch metrics 1402 and constant branch metrics 1404. FIG. 14 shows the final 8-state transformed trellis after also collecting common constant terms at the output of the ACS units and normalizing all metric components 1402, 1404 by a factor of two. Similarly, it can be seen, by applying the time invariance transformation, that an equivalent representation of the first summation term in equation (22) is also: $\begin{matrix} {{- {\sum\limits_{n}\left\{ {{y_{2n}\left( {a_{2n} + a_{{2n} - 1} - a_{{2n} - 2} - a_{{2n} - 3}} \right)} + {y_{{2n} + 1}\left( {a_{{2n} + 1} + a_{2n} - a_{{2n} - 1} - a_{{2n} - 2}} \right)}} \right\}}} = {- {\sum\limits_{n}\left\{ {{a_{2n}W_{2n}} + {a_{{2n} + 1}W_{{2n} + 1}}} \right\}}}} & (26) \end{matrix}$

where W_(n)=y_(n)+y_(n+1)−y_(n+2)−y_(n+3) can be interpreted as the output of a matched-filter with a response matched to (1−D²)(1+D). In this case the metric becomes: $\begin{matrix} {J = {{- {\sum\limits_{n}\left\{ {{a_{2n}W_{2n}} + {a_{{2n} + 1}W_{{2n} + 1}}} \right\}}} + {\sum\limits_{n}\left( {{{- 2}a_{2n}a_{{2n} - 2}} - {a_{2n}a_{{2n} - 3}} - {2a_{{2n} + 1}a_{{2n} - 1}} + {a_{{2n} - 2}a_{{2n} - 3}} + {a_{{2n} + 1}a_{2n}} - {a_{{2n} + 1}a_{{2n} - 2}}} \right)}}} & (27) \end{matrix}$

FIG. 15 shows a block diagram representation illustrating a generalized partial-response data channel including an EPR4 detector for EPR4 equalized signals using partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1500. As shown in FIG. 15, generalized partial-response data channel 1500 includes the low pass filter 102 and an extended partial response class 4 (EPR4) equalizer 1504 followed by a partial matched filter (1−D⁻²) 1508, and a corresponding 8-state EPR4 detector 1510. The output of EPR4 equalizer 1504 is an equalized signal output y_(n). The partial matched filter (1−D⁻²) 1508 provides an output Z_(n). The 8-state EPR4 detector 1510 provides output decisions a_(n).

FIG. 16 shows a block diagram representation illustrating a generalized partial-response data channel including an EPR4 detector for EPR4 equalized signals using matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1600. As shown in FIG. 16, generalized partial-response data channel 1600 includes the low pass filter 102 and an extended partial response class 4 (EPR4) equalizer 1604 followed by a matched filter (1−D⁻²)(1−D⁻¹) 1608, and a corresponding 8-state EPR4 detector 1610. The output of EPR4 equalizer 1604 is an equalized signal output y_(n). The matched filter (1−D⁻²)(1−D⁻¹) 1608 provides an output W_(n). The 8-state EPR4 detector 1610 provides output decisions a_(n). The matched filter (1−D⁻²)(1−D⁻¹) 1608 facilitates the transformation of the trellis according to the metric in equation (27). FIG. 16 includes the same detector as in FIG. 15.

FIG. 17 illustrates an EPR4 8-state 2T trellis with matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1700 including data dependent branch metrics 1702 and constant branch metrics 1704. FIG. 17 shows the 8-state transformed trellis 1700 with two samples per branch that minimizes the equivalent metric of equation (27). Note that in all cases the data dependent terms 1702 of the branch metrics are added at the output of the ACS units and that there are only 12 non-zero branch constants out of the maximum 32 possible ones.

The NPML 16-state detector target with two predictor coefficients is given in equation (14). A Viterbi detector operating on two samples, Y_(2n), Y_(2n+1), at a time, will find the sequence {ân} that minimizes the metric in equation (19). As previously described, the first summation term in equation (19) depends on the channel samples and represents the time-varying or data dependent component of the branch metric. The second summation term depends only on data symbols and represents the constant component of the branch metric. Applying the time-invariance transformation we obtain the following equivalent matched-filter metric: $\begin{matrix} {J = {{- {\sum\limits_{n}\left\{ {{\left( {a_{2n} + a_{{2n} - 1}} \right)Z_{2n}} + {\left( {a_{{2n} + 1} + a_{2n}} \right)Z_{{2n} + 1}}} \right\}}} + {\sum\limits_{n}\left( {{s_{1}a_{2n}a_{{2n} - 1}} + {s_{2}a_{2n}a_{{2n} - 2}} + {s_{3}a_{2n}a_{{2n} - 3}} + {s_{4}a_{2n}a_{{2n} - 4}} + {s_{1}a_{{2n} - 1}a_{{2n} - 2}} + {s_{2}a_{{2n} + 1}a_{{2n} - 1}} + {s_{3}a_{{2n} - 1}a_{{2n} - 4}} + {s_{4}a_{{2n} + 1}a_{{2n} - 3}}} \right\}}}} & (28) \end{matrix}$

where Z_(2n) can be interpreted as the output of a partial matched-filter with a response matched to P(D)(1−D).

Referring to FIGS. 1, 2, and 18, FIG. 18 illustrates a NPML 16-state 2T trellis with partial matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1800 including data dependent branch metrics 1802 and constant branch metrics 1804. FIG. 1 shows the block diagram of a PR4 equalizer 104 followed by whitening/predictor filter 1+p1D+p2D² 106, partial matched filter (1−D⁻¹)(1+p1D⁻¹+p2D⁻²) 108, and the corresponding 16-state noise-predictive maximum-likelihood (NPML) detector 110. The partial matched-filter (1−D⁻¹)(1+p1 D⁻¹+p2D⁻²) facilitates the transformation of the trellis according to the metric in equation (28). FIG. 18 shows the particular 16-state trellis 1800 that minimizes the metric in equation (28) after constant terms 1804 have been collected at the output of the ACS units by applying the distributive law min(a+x,b+x)=min(a,b)+x and adding Z_(2n)+Z_(2n+1) to all the state metrics and normalizing all metric components by a factor of two. In FIG. 2 the constants b, c, d are given by

b=s₁−s₄

c=s₁+s₄

d=−s₁−s₂  (29)

In FIG. 18, the trellis 1800 requires only 40 branch adders instead of 64. Furthermore, there are 12 additions with data dependent or time-varying terms, 1802 and 8 additions with constant terms 1804 following the ACS unit. An equivalent metric realization can be obtained by applying a full matched-filter transformation to the metric in equation (28). By applying the time-invariance transformation the following equivalent matched-filter metric is obtained: $\begin{matrix} {J = {{- {\sum\limits_{n}\left\{ {{a_{2n}W_{2n}} + {a_{{2n} + 1}W_{{2n} + 1}}} \right\}}} + {\sum\limits_{n}\left( {{s_{1}a_{2n}a_{{2n} - 1}} + {s_{2}a_{2n}a_{{2n} - 2}} + {s_{3}a_{2n}a_{{2n} - 3}} + {s_{4}a_{2n}a_{{2n} - 4}} + {s_{1}a_{{2n} - 1}a_{{2n} - 2}} + {s_{2}a_{{2n} + 1}a_{{2n} - 1}} + {s_{3}a_{{2n} - 1}a_{{2n} - 4}} + {s_{4}a_{{2n} + 1}a_{{2n} - 3}}} \right\}}}} & (30) \end{matrix}$

Referring to FIGS. 6 and 19, FIG. 19 illustrates a NPML 16-state 2T trellis with matched filter metric in accordance with the preferred embodiment generally designated by the reference character 1900 including data dependent branch metrics 1902 and constant branch metrics 1904. FIG. 6 shows the PR4 equalizer 104 followed by whitening/predictor filter 1+p1D+p2D² 106, matched filter (1+p1D⁻¹+p2D⁻²)(1−D⁻²) 608, corresponding 16-state noise-predictive maximum-likelihood (NPML) detector 610. The matched filter (1+p1D⁻¹+p2D⁻²)(1−D⁻²) 608 facilitates the transformation of the trellis according to the metric in equation (28). FIG. 19 shows the 16-state trellis 1900 after adding W_(2n)+W_(2n+1) to all the state metrics and normalizing all metric components by a factor of two. The trellis in FIG. 19 again requires only 40 branch adders instead of 64. Furthermore, there are 12 additions with data dependent terms 1902, and 8 additions with constant terms 1904 following the ACS unit.

Referring now to FIGS. 20 and 21, there are shown add compare select (ACS) units 2000 and 2100 in accordance with the preferred embodiment. In the conventional Viterbi detector, the add compare select unit in a general form must add three terms and compare then with the sum of three other terms and select the result with minimum distance. In accordance with the preferred embodiment, a method is provided to change the addition of three terms to two terms for the general form and thus a speed advantage is provided. ACS units 2000 and 2100 in accordance with the preferred embodiment also provide add and compare operations in parallel for additional speed advantage.

Referring also to FIG. 10, the ACS unit 2000 in FIG. 20 illustrates a hardware implementation for states 0:7 of FIG. 10. ACS unit 2000 includes a compare 2002 for comparing state metric input values SM_X, SM_Y, a pair of adds 2004 and 2006 for adding the state metric input values SM_X, SM_Y and the data dependent term W_(n). A pair of shifts 2008 and 2010 couple the output of adds 2004 and 2006 to a 2:1 multiplexer 2012. Shifts 2008 and 2010 receive a shift control input for providing metric bounding to avoid underflow. Shifts 2008 and 2010 shift all state metric values when recentering around zero is required. Multiplexer 2012 select between the two outputs of adds 2004 and 2006 controlled by t he output of compare 2002 applied to a select (SEL) input. A latch 2014 connected to the multiplexer 2012 holds the state metric value.

Referring now to FIG. 21, the ACS unit 2100 illustrates a hardware implementation for states 8:15 of FIG. 10. ACS unit 2100 includes a compare 2102 for comparing state metric input values SM_X, SM¹³ Y, a pair of adds 2104 and 2106 for adding the state metric input values SM_X, SM_Y and the constant terms −s₁,−s₂,−s₃,−s₄. The compare 2102 includes a hard shift 2120 that is the same for all programmable polynomials and is hard coded. The compare 2102 and hard shift 2120 provides an add for one branch and then a compare between the resultant branches. The compare 2102 and hard shift 2120 operates as fast as the normal compare operation. A pair of shifts 2108 and 2110 couple the output of adds 2104 and 2106 to a 2:1 multiplexer 2112. Shifts 2108 and 2110 receive a shift control input for providing metric bounding to avoid underflow. Shifts 2108 and 2110 shift all state metric values when recentering around zero is required. Multiplexer 2112 select between the two outputs of adds 2104 and 2106 controlled by the output of compare 2102 applied to a select (SEL) input. A latch 2114 connected to the multiplexer 2112 holds the state metric value.

While the present invention has been described with reference to the details of the embodiments of the invention shown in the drawing, these details are not intended to limit the scope of the invention as claimed in the appended claims. 

What is claimed is:
 1. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals in a Viterbi detector including 2^(L) states; where L is a non-zero positive integer value; said method comprising the steps of: transforming branch metric terms to shift all time varying terms and some constant terms after an add compare select (ACS) unit; said time varying terms being expressed as outputs W_(n) of a matched filter or said time varying terms being expressed as outputs Z_(n) of a partial matched filter; minimizing a total number of non-zero constants on trellis branches; and adding said shifted time varying terms and said shifted constant terms directly to state metric terms; performing a maximum of 2^(L−1) additions of said shifted time varying terms.
 2. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 1 wherein said time varying terms are expressed as said outputs W_(n) of said matched filter of the form (1+p1D⁻¹+p2D⁻²)(1−D⁻²) where p1 and p2 are arbitrary numbers, not limited to integers; and wherein the step of adding said shifted constant terms directly to state metric terms includes the steps of adding predefined combinations of s₁, s₂, s₃, s₄, where s₁=p₁(p₂+1); s₂=−(1−p₂)²−p₁ ², s₃=−p₁(p₂+1), and s₄=−p₂.
 3. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 1 wherein said time varying terms are expressed as said outputs Z_(n) of said partial matched filter of the form (1+p1D⁻¹+p2D⁻²)(1−D⁻¹) where p1 and p2 are arbitrary real numbers, not limited to integers; and wherein the step of adding said shifted constant terms directly to state metric terms includes the steps of adding predefined combinations of s₁, s₂, s₄, where s₁=p₁(p₂+1); s₂=−(1−p₂)²−p₁ ², and s₄=−p₂.
 4. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 1 wherein the step of adding said shifted time varying terms and said shifted constant terms directly to state metric terms includes the step of performing a maximum of 2^(L−1) additions of said shifted constant terms.
 5. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 1 wherein the step of adding said shifted time varying terms and said shifted constant terms directly to state metric terms includes the step of processing multiple samples per trellis branch.
 6. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 1 includes the step of identifying a set of branch metric constants with a maximum number of zeros.
 7. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 1 wherein the step of transforming branch metric terms to shift all time varying terms and some constant terms after an add compare select (ACS) unit includes the step of applying a time-invariance transformation to a generalized partial response metric to obtain an equivalent metric.
 8. A method for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 1 wherein the step of transforming branch metric terms to shift all time varying terms and some constant terms after an add compare select (ACS) unit includes the step of applying a distributive law min(a+x, b+x)=min(a,b)+x.
 9. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals in a Viterbi detector including 2^(L) states; where L is a non-zero positive integer value; and including a partial matched filter or a matched filter comprising: Viterbi detection trellis having transformed branch metric terms to shift all time varying terms and some constant terms after an add compare select (ACS) unit; said time varying terms being expressed as outputs W_(n) of a matched filter or said time varying terms being expressed as outputs Z_(n) of a partial matched filter; and said transformed branch metric terms for minimizing a total number of non-zero constants on trellis branches; and said Viterbi detection trellis having branch adders for adding said shifted time varying terms and said shifted constant terms directly to state metric terms; said branch adders for adding a maximum of 2^(L−1) of said shifted time varying terms.
 10. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 9 wherein said time varying terms include said outputs W_(n) of said matched filter of the form (1+p1D⁻¹+p2D⁻²)(1−D⁻²) where p1 and p2 are arbitrary real numbers, not limited to integers.
 11. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 9 wherein said time varying terms include said outputs Z_(n) of said partial matched filter of the form (1+p1D⁻¹+p2D⁻²)(1−D⁻¹) where p1and p2 are arbitrary real numbers, not limited to integers.
 12. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 9 wherein said minimum number of non-zero constants on trellis branches are identified by applying a time-invariance property of the Viterbi detector without resorting to heuristics.
 13. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 12 wherein said time-invariance property holds for Viterbi detectors for processing multiple samples per trellis-branch, thus allowing implementations at a desired speed.
 14. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 9 wherein said Viterbi detection trellis having said transformed branch metric terms is provided by identifying a set of branch metric constants with a maximum number of zeros.
 15. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 9 wherein said Viterbi detection trellis having said branch adders for adding said shifted time varying terms and said shifted constant terms directly to state metric terms includes said branch adders for adding a maximum of 2^(L−1) additions of said shifted constant terms.
 16. Apparatus for implementing high-speed and area efficient architectures for Viterbi detection of generalized partial response signals as recited in claim 9 wherein said Viterbi detection trellis having said transformed branch metric terms provided by applying a distributive law min(a+x, b+x)=min(a,b)+x. 